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Dissimilarity Measure



Overview about dissimilarity and distance measure.

1. Euclidian Distance


$$ \large \displaystyle d(x,y) \mapsto \|x-y\|_2 = \left[\sum_{i}^{n}(x_i-y_i)^2\right]^\frac{1}{2} = \sqrt{\sum_{i}^{n}(x_i-y_i)^2} $$

2. Manhattan Distance


$$ \large \displaystyle d(x,y) \mapsto \|x-y\|_1 = \sum_{i}^{n}|x_i-y_i| $$

3. Chebyshev Distance


$$ \large \displaystyle d(x,y) \mapsto \|x-y\|_\infty = \lim_{p\to\infty} \left(\sum_{i}^{n}|x_i-y_i|^p\right)^\frac{1}{p} = \overset{n}{\underset{i}{\max}}|x_i-y_i| $$

4. Minkowski Distance


$$ \large \displaystyle d(x,y) \mapsto \|x-y\|_p = \left(\sum_{i}^{n}|x_i-y_i|^p\right)^\frac{1}{p} $$